Wave trains, self-oscillations and synchronization in discrete media

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed, as well as the critical coupling and the critical separation of time scales for propagation failure. It describes stable wave train generation by repeated firing at a boundary. In self-oscillatory media, wave trains persist but synchronization phenomena arise. An equation describing the evolution of the oscillator phases is derived.Comment: to appear in Physica D: Nonlinear Phenomen

Asymptotic construction of pulses in the Hodgkin Huxley model for myelinated nerves

A quantitative description of pulses and wave trains in the spatially discrete Hodgkin-Huxley model for myelinated nerves is given. Predictions of the shape and speed of the waves and the thresholds for propagation failure are obtained. Our asymptotic predictions agree quite well with numerical solutions of the model and describe wave patterns generated by repeated firing at a boundary.Comment: to appear in Phys. Rev.

Depinning transitions in discrete reaction-diffusion equations

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.Comment: 27 pages, 12 figures, to appear in SIAM J. Appl. Mat

Theory of defect dynamics in graphene: defect groupings and their stability

We use our theory of periodized discrete elasticity to characterize defects in graphene as the cores of dislocations or groups of dislocations. Earlier numerical implementations of the theory predicted some of the simpler defect groupings observed in subsequent Transmission Electron Microscope experiments. Here we derive the more complicated defect groupings of three or four defect pairs from our theory, show that they correspond to the cores of two pairs of dislocation dipoles and ascertain their stability.Comment: 11 pages, 7 figures; replaced figure

Balancing the Migration of Virtual Network Functions with Replications in Data Centers

The Network Function Virtualization (NFV) paradigm is enabling flexibility, programmability and implementation of traditional network functions into generic hardware, in form of the so-called Virtual Network Functions (VNFs). Today, cloud service providers use Virtual Machines (VMs) for the instantiation of VNFs in the data center (DC) networks. To instantiate multiple VNFs in a typical scenario of Service Function Chains (SFCs), many important objectives need to be met simultaneously, such as server load balancing, energy efficiency and service execution time. The well-known \emph{VNF placement} problem requires solutions that often consider \emph{migration} of virtual machines (VMs) to meet this objectives. Ongoing efforts, for instance, are making a strong case for migrations to minimize energy consumption, while showing that attention needs to be paid to the Quality of Service (QoS) due to service interruptions caused by migrations. To balance the server allocation strategies and QoS, we propose using \emph{replications} of VNFs to reduce migrations in DC networks. We propose a Linear Programming (LP) model to study a trade-off between replications, which while beneficial to QoS require additional server resources, and migrations, which while beneficial to server load management can adversely impact the QoS. The results show that, for a given objective, the replications can reduce the number of migrations and can also enable a better server and data center network load balancing

Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

Does child labor always decrease with income ? an evaluation in the context of a development program in Nicaragua

This paper investigates the relationship of household income with child labor. The analysis uses a rich dataset obtained in the context of a conditional cash transfer program in a poor region of Nicaragua in 2005 and 2006. The program has a strong productive emphasis and seeks to diversify the work portfolio of beneficiaries while imposing conditionalities on the household. The author develops a simple model that relates child labor to household income, preferences, and production technology. It turns out that child labor does not always decrease with income; the relationship is complex and exhibits an inverted-U shape. Applying the data to the model confirms that the relationship is concave when all children (8-15 years of age) are included in the sample. Expanding the analysis by stratifying the sample by age and gender shows that the relationship holds only for older children, both genders. The author investigates the effect of the conditional cash transfer program on child labor. The results show that the program has a decreasing effect on total hours of work for the full sample of children. Disentangling labor into two types - physically demanding labor and non-physical labor - reveals that the program has opposite effects on each type; it decreases physically demanding labor while increasing participation in non-physical (more intellectually oriented) tasks for children.Street Children,Youth and Governance,Labor Policies,Children and Youth,Labor Markets

Constructing solutions for a kinetic model of angiogenesis in annular domains

We prove existence and stability of solutions for a model of angiogenesis set in an annular region. Branching, anastomosis and extension of blood vessel tips are described by an integrodifferential kinetic equation of Fokker-Planck type supplemented with nonlocal boundary conditions and coupled to a diffusion problem with Neumann boundary conditions through the force field created by the tumor induced angiogenic factor and the flux of vessel tips. Our technique exploits balance equations, estimates of velocity decay and compactness results for kinetic operators, combined with gradient estimates of heat kernels for Neumann problems in non convex domains.Comment: to appear in Applied Mathematical Modellin

Self-sustained current oscillations in the kinetic theory of semiconductor superlattices

We present the first numerical solutions of a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. These conditions seamlessly become Ohm's law at the injecting contact and the zero charge boundary condition at the receiving contact when integrated over the wave vector. The time-dependent model is numerically solved for the distribution function by using the deterministic Weighted Particle Method. Numerical simulations are used to ascertain the convergence of the method. The numerical results confirm the validity of the Chapman-Enskog perturbation method used previously to derive generalized drift-diffusion equations for high electric fields because they agree very well with numerical solutions thereof.Comment: 26 pages, 16 figures, to appear in J. Comput. Phy

Statics and dynamics of a harmonic oscillator coupled to a one-dimensional Ising system

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the oscillator stable rest position as its order parameter. Secondly, for fast spins, the oscillator dynamics is described by an effective equation with a nonlinear friction term that drives the oscillator towards the stable equilibrium state.Comment: Proceedings of the 2010 Granada Semina